An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 4 N , 1 N># and the second is #F_2 = < 5 N, 9 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-21T11:17:06

The rate of acceleration #=4.48ms^-2# in the direction #48.0#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <4,1>+<5,9>#

#=<9,10>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/3<9,10> = <3, 10/3>#

The magnitude of the acceleration is

#||veca||=||<3,10/3>||#

#=sqrt((3)^2+(10/3)^2)#

#=sqrt(9+100/9)#

#=sqrt 181/3=4.48ms^-2#

The direction is #theta = arctan((10/3)/(3))#

The angle is in the 1st quadrant

#theta=arctan(10/9)=48.0#º